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Abstract:

A display system includes a display-color function image generator and a
DCF image converter. The DCF image generator generates a DCF image from a
source image. In the DCF image, each pixel is associated with a
respective DCF configured to convert an input value to a display color
value. The DCF image generator inputs values to respective DCFs to
convert the DCF image to a displayable image having pixels associated
with respective display colors.

Claims:

1. A display system comprising: a image generator configured to generate
from a source image a display color function (DCF) image having pixels
with respective associated DCFs, each of the DCFs being configured to
convert input values to respective display colors; and an image converter
configured to input respective values to the DCFs so as to yield
respective display color values to be associated with spatially
corresponding pixels of a displayable image.

2. A display system as recited in claim 1 wherein each of said DCFs
corresponds to a cumulative distribution of display colors characterizing
a source color at a corresponding spatial position of the source image.

3. A display system as recited in claim 2 wherein said image generator
includes a random matrix generator configured to generate said values
randomly using a spatial threshold quantization matrix associated with a
noise spectrum in a green-to-blue spatial color range.

4. A display system as recited in claim 3 further comprising printer
components configured to print said displayable image, the displayable
colors being Neugebauer primaries (NPs), the DCFs corresponding to
respective indexed cumulative distributions of NP area coverages.

5. A display system as recited in claim 4 wherein said DCF image
generator is configured to obtained said DCF image without first
explicitly generating an NP area coverage vector image.

6. A display method comprising: generating a display-color function (DCF)
image from a source image, the DCF image having pixels associated with
respective DCFs for converting input values to display colors; and
converting the DCF image to a displayable image having pixels associated
with respective display colors by inputting respective input values to
the DCFs to determine the display colors to be associated with spatially
corresponding pixels of said displayable image.

7. A display method as recited in claim 6 further comprising printing
said displayable image by depositing ink on a print medium, said
displayable colors being Neugebauer primaries (NPs), said DCFs
corresponding to respective indexed cumulative distributions of NP area
coverages.

8. A display method as recited in claim 7 wherein said generating
includes generating the cumulative distributions without previously
generating a NP area coverage vector image corresponding to said source
image.

11. A product comprising computer-readable storage media encoded with
code configured to, when executed by a processor: generate a
display-color function (DCF) image from a source image, said DCF image
having pixels with respective DCFs for converting input values to display
color values; and convert the DCF image to a displayable image having
pixels with associated respective display colors determined by inputting
respective input values to the respective DCFs.

12. A product as recited in claim 11 wherein said display colors are
Neugebauer primaries (NPs).

13. A product as recited in claim 12 wherein each DCF corresponds to a
respective cumulative distribution of NP area coverages.

14. A product as recited in claim 11 wherein said code is configured to
generate said input values randomly so as to conform to a spatial
quantization matrix characterized by a spatial noise spectrum in the
green-to-blue color range.

15. A product as recited in claim 12 wherein said code is configured to
generate said DCF image without first explicitly generating an NP area
coverage vector image corresponding to said source image.

Description:

BACKGROUND

[0001] Inkjet printing is often used to reproduce continuous-tone, e.g.,
photographic, images using a limited number of ink colors. Inkjet
printers commonly use a CMYK color model, e.g., in which the ink colors
are cyan, magenta, yellow, and black. Ink colors can be 1) blended or 2)
spatially averaged (or both) to provide colors not represented by the
individual inks. For example, human perception will spatially average a
pattern of red and yellow pixels to yield a perception (optical illusion)
of orange. The yellow dots can be achieved using yellow ink, while the
red dots can be achieved by blending or overlaying magenta and yellow
inks.

[0002] "Continuous-tone" images may be converted to a printable, e.g.,
"half-tone", image form suitable for inkjet printing progressively. The
difference between the color in the continuous-tone image and its
"approximation" color in the target image is called a "quantization
residual" or "error". "Error diffusion" is a technique in which the
quantization residuals of previously processed pixels are distributed to
neighboring pixels so that the target image will closely match the
continuous tone image. Thus, for example, error diffusion can make it
more likely that some neighbors of a red pixel are yellow where the
objective is to provide a perception of orange.

BRIEF DESCRIPTION OF THE DRAWINGS

[0003]FIG. 1 is a schematic diagram of a display system in accordance
with an embodiment.

[0004]FIG. 2 is a flow chart of a process implemented by the display
system of FIG. 1.

[0005]FIG. 3 depicts images, values, and functions used to explain
certain concepts pertaining to the display system of FIG. 1.

[0006]FIG. 4 is a schematic diagram of an inkjet printing system in
accordance with an embodiment.

[0007]FIG. 5 is a flow chart of a process implemented by the printing
system of FIG. 4.

[0008] FIG. 6 is a table corresponding to a Neugebauer primary vector for
a light pink.

[0011] A display system 100 includes a display-color function (DCF) image
generator 102 and a DCF image converter 104. Display system 100 is
configured to implement a process 200 flow-charted in FIG. 2. At process
segment 201, generator 102 generates the DCF image from a source image.
At process segment 201, converter 104 converts the DCF image into a
displayable image. Display system 100 and process 200 provide
high-performance, high-quality conversions of source images, as well as
for efficient color management. For example, display color functions can
be performed in parallel to provide for higher performance image
conversion than that obtainable using comparable conversions using
error-diffusion (which requires some output colors to be computed before
others, thereby limiting parallelism).

[0012] Herein, "displayed image" and "printed image" refer to
human-viewable (HV) images, while "source image", "display-color function
image", and "displayable image" refer to computer-readable
representations of HV-images. Typically, there is also a human-viewable
version of the source image, e.g., a source image on a monitor. Images of
various dimensionalities are provided for, including two-dimensional and
three-dimensional images. The images can be still images, moving images,
or frames of moving images. In various embodiments, by way of example and
not of limitation, the displayed image can be printed, lithographed,
laser-etched, or displayed on an LCD or e-ink display, or displayed as a
hologram. In fact, the display can be in the form of an array of just
about any luminescent or reflecting objects, e.g., holiday lights or
metallic gold and other metallic color stars.

[0013] A source image can be defined in any color space and may be a
continuous tone image. For expository purposes, a source image 301 is
represented in FIG. 3 having a 2×2 block of pixels; pixels S11,
S12, and S21 are assigned a blue teal color, while pixel S22 is assigned
a green teal color.

[0014] Herein, a "displayable image" is an image that can be displayed,
e.g., on a monitor or by printing it on paper. The displayable images
referred to herein tend to be non-continuous-tone images. The displayable
image can be a digital representation that corresponds pixel-by-pixel
with the to-be-displayed image.

[0015] A "display color" is a color that can be represented by a single
pixel (without spatial averaging). A display color can be an elemental
color (e.g., red in an RGB display system or cyan in a CMYK system), or a
composite color (e.g., teal=blue+green in an RGB color system or
red=magenta+cyan in a CMYK system). While "elemental" colors are referred
to as "primary" colors elsewhere in the literature; herein, the term
"primary" is used in the phrase "Neugebauer primaries"; Neugebauer
primaries typically include both elemental and composite colors (but
exclude colors that can only be perceived using spatial averaging).

[0016] For expository purposes, a displayable image 303 is shown in FIG. 3
having a 2×2 block of pixels D11-D22 corresponding to pixels
S11-S22 in source image 301. Pixels D11 and D12 are assigned a display
blue color, and pixels D21 and D22 are assigned a display green color.
While many embodiments provide for a wider range of display colors, for
expository purposes, assume that image 303 is to be displayed on a system
that provides for red, green, and blue colors to be displayed without any
control over intensity.

[0017] Herein, a "display-color function image" or "DCF image" is an image
having pixels wherein each pixel is assigned a display-color function.
Herein, a DCF (e.g., y=f(x)) is used to convert an input numerical value
(x) to a numerical or vector representation (y) of a display color. A DCF
can typically and conveniently be represented by a look-up table, e.g.,
with the numerical values x as the indices and precalculated display
colors y as the output. For example, a DCF image 305 is shown in FIG. 3
with a 2×2 block of pixels F11-F22 corresponding to block S11-S22
of source image 301 and block D11-D22 of displayable image 303. Pixel F11
is associated with a blue-teal DCF 307. Pixel F22 is associated with a
green-teal DCF 309. The DCFs for pixels F12 and F21 are not shown
separately in FIG. 3. However, their DCFs are identical to DCF 307 since
pixels F11, F12, and F13 all correspond to blue-teal pixels in source
image 301.

[0018] Each DCF is configured to convert an input value to a display color
(for the corresponding pixel). For example, DCF 307 is a look-up table
configured to convert integer values 1-8 into (computer-readable
representations of) red, green, and blue display colors. In the case of
DCF 307, 1 is converted to red, 2-4 are converted to green, and 5-8 are
converted to blue. Note that some display colors may correspond to more
than one input value and some display colors may correspond to more input
values than other display colors. In some DCFs, not all display colors
are represented; e.g., all inputs to a red DCF might yield red. In DCF
307, blue appears in more instances than green because blue-teal is
predominantly blue. In contrast, teal green DCF 309 contains more green
than blue. A single value is associated with red in both DC-LUTS 307 and
309, as red is only weakly represented in teal blue and teal green.

[0019] Each DCF in DCF image 305 corresponds to a color in source image
301. At least as a first approximation, the proportions in which display
colors appear in a DCF may correspond to the proportions those display
colors would appear in a sufficiently large block in a displayed image
that a viewer applying spatial averaging would perceive as the
corresponding source color. Thus, the 4:3:1 representation of
blue:green:red in DCF 307 is an area coverage distribution for teal blue.
In practice, DCFs with many more than eight entries each would be
required to precisely represent a continuous-tone source image. For
example, 8-bit DCFs (256-entry look-up tables) could be used.

[0020] A source image can be converted to a display-space image having
pixels associated with respective display-space color vectors that can be
interpreted to indicate the relative regional (e.g., area) cover
distributions with which the display colors would be represented in a
color block corresponding to the source color for the pixel. A
display-color vector can be converted to a DCF by 1) stacking the
distributions to form a cumulative distribution; and 2) indexing the
cumulative distribution to form a look-up table. This causes certain
input value ranges to correspond to certain respective display colors.
For example, in DCF 307, input values 5-8 correspond to green while input
values 1-4 do not. In DCFs 307 and 309 distributions are ordered from
smallest (red) to greatest (blue for DCF 307 and green for DCF 309). In
alternative embodiments, other ordering schemes are used; for example,
display colors can be assigned index values and the display colors can be
ordered according to the index numbers in a DCF. In the interest of
efficiency, generator 102 computes DCFs directly from the source image
without requiring an explicit intermediate determination of a
display-space vector image.

[0021] While DCFs may be viewed as corresponding to regional (area)
coverage distributions, display system 100 treats them as probability
distributions corresponding to a likelihood that a pixel in the
displayable image will be associated with a particular display color. For
example, according to DCF 307, assuming all DCF input values are equally
probable, there is a 4/8 (50%) a priori likelihood that display pixel D11
will be assigned a blue color and a 3/8 (37.5%) a priori likelihood it
will be assigned a green color.

[0022] Converter 104 inputs values into respective DCFs to generate a
displayable image. For example, input matrix 311 includes values V11-V22
to be applied respectively to the DCFs of pixels F11-F22 of DCF image
305. Thus, the value V11=7 is input to DCF 307 so that pixel D11 is
assigned blue, and the value V22=6 is input to DCF 309 so that pixel D22
is assigned green. The values V12=5 and V21=3 result in blue and green
being respectively assigned to pixels D12 and D21.

[0023] Some generally displeasing conversion artifacts can be avoided by
selecting the input values randomly. For example, if a fixed pattern of
values is applied to different blocks of a DCF image, so a human viewer
may perceive repetitive patterns not present in the source image. A
random selection of input values may avoid such repetitiveness.

[0024] However, random input values can result in clustering of minority
display colors (e.g., red in teal blue and teal green), where a more
uniform distribution of minority colors may give a more uniform and
pleasing appearance. Such clustering can be rendered less likely by
varying the quantization threshold for the random input values
pixel-by-pixel. For example, the chances are 1:8 that a randomly selected
integer value from 1-8 will result in a red pixel. This corresponds to a
quantization threshold of 1. If the quantization threshold is set to two,
the random input value will be an even number, in which case, the
corresponding pixel cannot be red. Thus, varying quantization thresholds
can be used to minimize clustering and provide a more uniform
distribution. Note that image generator 102 may pre-compensate for the
reduced presence of minority colors when quantization thresholds are
varied.

[0025] Techniques have been developed for reducing clustering and
low-spatial-frequency conversion artifacts in monochrome images. Due to
the reduction of spatial low frequency spectral characteristics, the
random input values can be said to be characterized by a green-to-blue
noise color range (as green light and blue light tend to have lower low
frequency content than white light). These techniques have been applied
to individual color planes for use in color image conversions. Different
thresholding patterns (matrices) are typically used for different color
planes to minimize Moire and other perceptual artifacts.

[0026] However, embodiments herein can use a single quantization threshold
matrix for color image conversion. This avoids the perceptual artifacts
that arise from the interaction of multiple matrices associated with
multiple color planes. Also, using a single quantization matrix can
result in a performance advantage over color conversion techniques that
use multiple quantization threshold matrices.

[0027] Display system 100 provides a substantial performance advantage
over systems that employ error diffusion. From the algorithm point of
view, all pixels are independent of each other and can be processed in
any order and all at the same time. This means that, in some cases,
depending on the size of the image relative to the degree of parallelism
obtainable by the image converter (e.g., a graphics processing unit), all
the pixels of an image may be processed in parallel. In other cases,
e.g., when memory or processing core limitations prevent an entire image
from being processed at once, the image can be segmented into blocks and
all of a single block's pixels that are processed in one cycle and the
entire image can be processed in as many cycles as there are blocks.

[0028] An inkjet printing system 400 applies the foregoing principles in
the context of a Neugebauer primary (NP) area coverage color space 401 to
achieve accurate image control as well as high-performance, high-quality
color printing. In particular, in system 400, the DCFs are based on
Neugebauer primary cumulative distributions (NPCDs).

[0029] Printing system 400 has printer components 402 configured to print
said displayable image. Components 402 include printheads 403 that can
deliver inks 405 onto a human-viewable (HV) print media 407. System 400
includes print mechanisms 409 for moving media 407 longitudinally
relative to printheads 403 and for moving printheads 403 transversely
relative to print media 407. System 400 includes a colorimeter 411 for
sensing the colors of a color characterization chart output on a print
medium for characterizing NP color space 401.

[0031] Spatial tuner 435 permits selection of various
quantization-threshold matrices that can be used by random matrix
generator 437. Available matrices include a white-noise matrix 461, a
green-noise matrix 463, and a blue-noise matrix 465. These matrices can
be defined in terms of tunable parameters that can be adjusted, for
example, to provide matrices that are intermediate between green and blue
and that have more or less sharp peaks. A blue-noise matrix can be
selected for print media, e.g., non-porous print media, for which the
mixing of inks from adjacent pixels can be strictly controlled. A green
noise matrix may be selected for print media, e.g., porous print media,
for which ink from adjacent pixels may mix. In the later case, colors in
the converted image may be clustered to minimized the somewhat
unpredictable mixing of different colors from adjacent pixels; in such a
case, a green-noise matrix may better achieve the desired pixel
clustering.

[0032] A process 500, flow charted in FIG. 5, is implemented by system 400
at least in part by executing code 427. Process 500 includes three
phases, characterization and setup phase 510, image conversion 520, and
printing 530. Characterization and setup phase 510 begins with a
characterization print. This involves printing a preset characterization
image. The characterization image can include an array of squares, with
each square corresponding to a different combination of number of drops
and inks. For example, if there are four ink colors, e.g., cyan, magenta,
yellow and black, and three drop values (zero drops, one drop, two drops)
per color, then there can be 34=81 possible Neugebauer primaries,
each represented by a respective square. Other numbers of drop sizes and
ink colors (e.g., including light cyan, light magenta, red, green, blue,
white, gold, silver, and other metallics) can be used.

[0033] The squares can be arranged with adjacent boundaries to test for
inter-pixel bleeding; alternatively, patterns devoted to testing for
inter-pixel bleeding can be used. Such characterization can be done each
time a new media type is used or the ink is changed so that the effects
of media type, ink variations, as well as other factors are taken into
account in characterizing the NP color space. A more common approach uses
ramps of single inks at various amounts as well as ramps of some sub-set
of secondaries and tertiaries. The ramps help detect both where bleeding
occurs as well as where adding more ink no longer helps in terms of
reaching further in color space.

[0034] At process segment 512, the characterization print is analyzed,
e.g., using colorimeter 411. The measured colors of the squares
characterize the NP color space at process segment 513. Each NP can be
mapped to a color of a standard color space and to the print commands
used to produce the display primary. In addition, inter-pixel blending
can be analyzed to determine which color noise matrix may be selected,
also at process segment 513.

[0035] In the case of blue-noise, dispersed-dot dither patterns are
constructed by isolating minority pixels as homogeneously as possible
and, by doing so, a pattern composed predominantly of high-frequency
spectral components is produced. Blue-noise half-toning is preferred for
display devices that can accommodate isolated dots such as various video
displays and some print technologies such as ink-jet. For print marking
engines that cannot support isolated pixels dispersed-dot half-toning is
inappropriate. For such cases, clustered-dot half-toning is used to avoid
dot-gain instability. Green-noise halftones are clustered-dot blue noise
patterns. Such patterns enjoy the blue-noise properties of homogeneity
and lack of low frequency texture, but have clusters of minority pixels
on blue-noise centers. Green noise is composed predominantly of
mid-frequency spectral components. (Credit: this paragraph is adapted
from Daniel L. Lau, Robert Ulichney, and Gonzolo R. Arce "Fundamental
Characteristics of Halftone Textures: Blue-Noise and Green-Noise" in IEEE
Signal Processing Magazine, Vol. 20(2), pp. 28-38, July 2003.)

[0036] Image conversion phase 520 converts a source image 451 to a NP
printable (and, thus, displayable) image 455. This phase includes a
process segment 521 of converting a source image to an NPCD image (a type
of DCF image) 453, and a process segment 522 of converting NPCD image 453
to NP printable image 455. NPCD image 453 assigns an ordered cumulative
distribution of NP colors to each image pixel. For example, each NP can
be assigned an index number and NPs in the NPCD can be arranged in order
of their index numbers. Alternatively, the distribution can be in order
of increasing or decreasing area coverage or according to some other
order.

[0037] An NP area coverage vector 600 for a light-pink source color is
shown in tabular form in FIG. 6. Vector 600 is constituted by six NPs.
For example, vector component #1 corresponds to NP index 55, which
corresponds to one magenta drop; component #1 has an area coverage
proportion of 126 parts per (pp) 256 pixels. For another example,
component #5 corresponds to white (W), and thus to no drops. Component #5
has an 8:256 area coverage value. A corresponding area-coverage
distribution is shown in FIG. 7.

[0038] An NP cumulative area coverage distribution (NPCD) 800, shown in
FIG. 8, can be obtained by "stacking" the component area coverages (e.g.,
from FIG. 6). In NPCD 800, individual NP distributions are stacked from
least prevalent to most prevalent. Alternatively, other orders, e.g.,
according to index value, are used. As indicated by the large hollow
arrows in FIG. 8, NPCD 800 can be used as a DCF look-up table for
generating display colors as a function of input values.

[0039] Process segment 521 can be implemented by first converting to an NP
area coverage vector space image and then converting the NP area coverage
vector space image to an NPCD image. However, in system 400, there is a
direct conversion from the source image to the NPCD image without
explicitly forming an NP area coverage vector image. This conversion is
possible due to convexity being preserved between an NP-area-coverage
representation and an NPCD representation (i.e., a convex combination of
NP area-coverage vectors is a convex combination of NPCDs with the same
convex weights).

[0040] Process segment 522 involves converting the NPCD image to an NP
printable image. This can be a bit map of NP primaries or the print
commands used to generate the NP primaries. The NP printable image is
obtained by random sampling of NPCDs on a pixel-by-pixel basis or by
taking the spatially collocated counterparts of the noise threshold
matrices mentioned above. More specifically, the NPCD is treated as a
lookup table that converts a random input value to an NP for each image
pixel. The use of random input values effectively treats the NP area
coverages as probabilities and the NPCDs as cumulative probability
distribution functions.

[0041] The law of large numbers guarantees that if there is a sufficiently
large area of pixels with the same NP area coverage and the NPs at each
location are chosen randomly and respecting the NP area-coverage
probabilities, over the entire area the NP area coverage (computing the
distribution of NPs placed at each pixel randomly from the local NP area
coverages) is the same as the per-pixel NP area coverage. The larger the
area is, the closer these per-pixel NP area coverage and per-area NP area
coverage are.

[0042] For each image pixel, the set(s) of values from which a random
number is selected is determined by the selection of the quantization
threshold matrix noise color at process segment 513. At phase 530, the NP
printable image is printed to form printed image 440. Pixels assigned
higher quantization thresholds may be precluded from being mapped to
certain display color components of a cumulative distribution. For
example, as can be gleaned from FIG. 8, a quantization threshold of eight
will prevent display color component #6 form being assigned to the
respective pixel of the displayable image. Likewise, a quantization
threshold of 16 will preclude display color components #5 and #6 from
being assigned to the respective displayable image pixel. The loss of
opportunities for minority display colors to be represented in the
displayable image caused by variable threshold quantization can be
pre-compensated by image converter 431. Displayable image 455 can be used
to print printable image 455 to yield printed image 440 at process
segment and phase 430.

[0043] Herein, a "display system" is a system for converting source images
into displayable images. The display system can be completely defined in
hardware, but, in most cases, it is a combination of software and
hardware used to execute the software. The display system may or may not
include the display itself. Herein, "generator" and "converter", e.g.,
generators 102 and 437 and converters 104, 431, and 433, refer to
hardware or software-cum-hardware entities that generate or convert
images.

[0044] Herein, "image" encompasses 1) displayed images in the form of
human-viewable light-emitting or reflecting spatial distributions; and 2)
computer-readable representations of displayed images. Herein, "source
image" encompasses any image that can be converted to a displayable
image; herein, a typical source image is a continuous-tone image. Herein,
"displayable image" is an image having pixels having display colors
assigned to pixels to the exclusion of non-display colors; herein, a
typical displayable image is a half-tone image, i.e., an image that
requires spatially averaging to create a perception of some colors.

[0045] Herein, a "display-color function" (DCF) is a function for
generating values representing display colors as a function of an input
value; herein, a typical input value is randomly generated. Herein, a
"display-color function image" or "DCF image" is an image having pixels
with associated DCF functions; herein, a typical DCF function corresponds
to a cumulative distribution of display color components of a source
image color.

[0046] Herein, "spatial threshold quantization matrix" refers to a matrix
or array of values that define quantization thresholds for randomly
generated values, e.g., on a pixel-by-pixel basis. Such matrices are used
herein to shape the spatial frequencies associated with the random values
input to a DCF image to yield a displayable image. Such matrices can be
characterized by noise colors depending on how they affect low, middle,
and high spectral frequencies. In most cases herein, spatial threshold
quantization matrices characterized by spectral noise in the
green-to-blue color range provide the most uniform and visually pleasing
image conversions.

[0047] Herein, "display color" encompasses colors that can be displayed
directly without relying on spatial averaging by a human viewer. A
"display color value" is a vector or scalar value (e.g., an NP index)
representing a display color. Herein, "Neugebauer primary" or "NP" refers
to a display color determined according to a characterization procedure
detailed elsewhere in the literature. "Neugebauer primary (NP) area
coverage vector" refers to a vector of area or region coverage values
corresponding to a source color. "Neugebauer primary (NP) area coverage
vector image" refers to an image having pixels, each of which has a
respective NP area coverage vector assigned. "Neugebauer primary (NP)
cumulative area coverage distribution" or "NPCD" refers to an indexed
cumulative distribution corresponding to an NP area coverage vector. An
NPCD can be in the form of a look-up table and used as a DCF for
generating displayable images based on input values.

[0048] Herein, "processor" encompasses hardware entities including
electrically or optically conductive material that can be used to execute
computer-executable code. A processor can consist of part of an
integrated circuit, an entire integrated circuit, or multiple integrated
circuits. In the latter case, a processor can be distributed among
devices, e.g., between a computer and a printer of a printing system.
Herein, "computer-readable storage media" or "CR-media" refers to
non-transitory tangible media in which computer readable code can be
encoded. Signals and other non-transitory propagating phenomena are not
encompassed by the term "media" as used herein.

[0049] Herein, a "system" is a set of interacting elements, wherein the
elements can be, by way of example and not of limitation, mechanical
components, electrical elements, atoms, instructions encoded in storage
media, and process segments. Herein, a "product" is any man-made thing,
such as computer-readable storage media. In this specification, related
art is discussed for expository purposes. Related art labeled "prior
art", if any, is admitted prior art. Related art not labeled "prior art"
is not admitted prior art. The illustrated and other described
embodiments, as well as modifications thereto and variations thereupon
are within the scope of the following claims.